What Blender calls surfaces are more commonly referred to in computer graphics as patches. It makes sense to stick to the commonly-accepted terminology, particularly when talking with users of other software.

You previously saw how a NURBS curve consisted of a single row of any number of control points. A NURBS patch consists of an n-by-m grid of points, where n and m can be any positive integer (and not necessarily equal). The grid has a rectangular topology, but of course the points may be positioned anywhere in space, to shape the curve accordingly. The resulting object can look a bit like a mesh in edit mode, but it behaves very differently.

Start a new document, delete the default cube, bla-bla-bla, but stay in Object mode. Add a new NURBS surface: SHIFT + A →Surface→NURBS Surface. Switch to Edit mode, and find the Surface Context in the Properties window.

For NURBS curves, you previously had the “Cyclic: U” and “Endpoint: U” options for making the curve open or closed, and extending all the way to the endpoints or not. Now you also have “Cyclic: V” and “Endpoint: V”, because the surface has two dimensions, and you can control these settings independently along each dimension. Try checking just one Cyclic box at a time, and the patch turns into a closed ribbon shape along the corresponding dimension; check both, and it forms a solid object, shaped perhaps reminiscent of a pillow or an unusual loaf of bread.

As with the curve case, you can move selected points around to alter the shape of the curve, and adjust the “W” value of each point to control how strongly it attracts the curve. Radius-scaling and tilt settings are still adjustable, but don’t seem to achieve anything, since you can’t apply a bevel to a surface.

Adding and deleting points in a NURBS surface need to follow some rules. The irritating thing is, if you try to do things not in accordance with these rules, Blender will simply ignore you, with no error message.

Remember how I said that the control points form a n-by-m rectangular grid? Any addition or deletion of points must preserve this characteristic. Thus, you can only add or remove points an entire row or column at a time. For example, to extend the patch, you select all the points along one outermost edge of it, and press E to add the same number of new points. Or you can select all the points in two adjacent rows or columns, and use W →Subdivide to add a new row/column of points in-between. Similarly, you can only delete points by selecting an entire row or column of them at a time.

The first two options in the SHIFT + A →Surface menu are “NURBS Curve” and “NURBS Circle”. Try adding these objects; at first glance, they look exactly like the “Nurbs Curve” and “Nurbs Circle” entries in the SHIFT + A →Curve menu. However, regardless of appearances, these really are surfaces, not curves.

To observe the difference, ensure all points are selected, and now use E to extend the curve: this will create a whole row of new control points, instead of just one! As with the different options in the SHIFT + A →Curve menu, the ones in SHIFT + A →Surface offer premade objects for you to choose whichever is the most convenient starting point for the shape you actually want to create.